2. Researchers are designing an experiment to compare two diferenst types of running shoes, A and B, to investigate which type i
s better for minimizing running time for a one-mile run. The experiment will consist of distributing design is planned, with blocking by classification of runner. Random samples of 50 professional runners and wear either the type A shoe or the type B shoe, and their running times will be recorded for a one-mile run. (a) What is a statistical advantage of blocking by the classification of runner? the shoes to runners who are classified as either professional or recreational. A randomized block unners will be selected. Each runner within each classification will be randomly assigned to Blocana by the classi (b) Why is it important to randomize the type of shoe the runner will wear instead of allowing the runner to choose the shoe? GO ON TO THE NEXT PAGE. EER Describe the shape of a histogram created from the data of the two s of students combined. With no ndicaion oF ourliers A crnitr berwen 96-10 s. The data nas a epiend of tom veseun 35-15 avou 80. (e) Consider the pogulation of all tudents in honors biokogy classes in the high school's state who are given the times has a shape similar to the combined histogram of students at the high school, with mean 70 minutes and standard deviation 26.5 minutes. For random samples of 50 students taken from the population, describe the sampling distribution of the sample mean completion time. task of using the spreadsheet program to investigate the topic in genetics. The distribution of the completion GO ON TO THE NEXT PAGE eny part of this page egat 7-
2 a) In Randomized Block design there are two variables one is a blocking variable the other one will be the treatment variable. Here type of shoes is the treatment variable and the type of runner is the blocking variable. Blocking is the arrangement of subjects similar in certain characteristics in to a group. Here professional runners are different from recreational runners . Blocking is done to reduce variability within groups so that variability within blocks is less than the variability between blocks. Then, subjects within each block are randomly assigned one of the shoes.
b) Randomization is the process of assigning participants a specific treatment so that each participant has an equal chance of being assigned a shoe A or B. Randomization is done using random number generation and assignment is made according to the random numbers The main purpose of randomization is to eliminate biases. If the person in a group are allowed to choose the shoes they may choose their preferred one based on their past experience of using it or one variety will be preferred by most of the subjects in the group spoiling the entire purpose of the study. for e.g a group of professionals coming from a particular region prefers type A . If randomization is employed in such a situation almost half of the professionals coming from a particular region gets type A and the other half may get type B thus eliminating the personal biases in choice. This way we can eliminate any possible biases that may arise in the experiment. So randomization and blocking are important for a randomized block design in order to minimize bias in the responses.
The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) − b shifts the function b units downward. f (x + b) shifts the function b units to the left
